[[Lie algebras MOC]]
# Special linear Lie algebra

Let $\mathbb{K}$ be a [[field]] and $n \in \mathbb{N}$.
The **special linear Lie algebra** $\mathfrak{sl}_{n}\mathbb{K}$ is the [[Lie algebra]] realized by [[Trace|traceless]] $n \times n$ matrices under their [[linear commutator]]. #m/def/lie
It is a [[Lie subalgebra|subalgebra]] of [[General linear Lie algebra]].

## Special cases

- [[sl_2]] 

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